I'd like to know if there's a way to copy custom mapping preferences to a file that I can use on my other computer.

Thanks for your help. 

You can find all settings of Remote Buddy at

~/Library/Preferences/com.iospirit.remotebuddy.*

Remote Buddy creates a preference file for each remote control, so you 
can easily move them across computers.

Just make sure RB is not running on the target computer, then copy 
over the file from the source computer's

~/Library/Preferences/

to the same directory on the target computer.

Best regards, 
Felix Schwarz